This invention relates generally to a method of producing a superconductor having a MBa.sub.2 Cu.sub.4 O.sub.8 (M=a rare earth element) crystallographic phase and, more specifically, to a method of producing a superconductor of metal oxides having the following composition: (M.sub.1-x Ca.sub.x)(Ba.sub.1-y Sr.sub.y).sub.2 Cu.sub.4 O.sub.8 where M is the same as above and x and y each represent a positive number of less than 1.